OFFSET
1,5
COMMENTS
(Empricial) T(n,k)=Number of nXk matrices containing a defective permutation of 1..n*k in strictly increasing order rowwise and columnwise, with one permutation value omitted and one repeated (see example)
Formula is n*(n-1)*k*(k-1)/2 times n-th k-dimensional Catalan number
Table starts
.0.......0.............0....................0...........................0
.0.......4............30..................168.........................840
.0......30...........756................16632......................360360
.0.....168.........16632..............1729728...................199536480
.0.....840........360360............199536480................140229804000
.0....3960.......7876440..........25241364720.............118949931243000
.0...18018.....174594420........3445446284280..........117015012361447200
.0...80080....3926434512......500598983364480.......129624266420759510400
.0..350064...89492111280....76591644454765440....158211402715245473193600
.0.1511640.2064420294300.12237255920840932800.209298196564031904834960000
LINKS
R. H. Hardin, Table of n, a(n) for n=1..1000
EXAMPLE
Some solutions for 4X2
..2..4....1..4....1..3....1..3....2..5....1..3....1..3....2..4....1..2....1..3
..3..5....2..5....3..6....2..4....3..6....2..4....2..4....3..6....2..4....2..4
..5..7....6..7....4..7....4..6....4..7....4..5....4..7....5..7....3..5....4..7
..6..8....7..8....5..8....5..8....5..8....7..8....5..8....6..8....6..8....6..8
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Oct 10 2010
STATUS
approved